Normally we classify all arguments into one of two types: deductive and inductive.
Deductive arguments are those meant to work because of their pattern alone, so
that if the premises are true the conclusion could not be false. All
other arguments are considered to be inductive (or just non-deductive), and
these are meant to work because of the actual information in the premises so
that if the premises are true the conclusion is not likely to be false.
The difference is between certainty (we can be sure the conclusion is correct)
and probability (we can bet on the conclusion being correct).

We now go one step further. A deductive argument with the right form is
considered to be valid, regardless of the
truth of the premises. When the premises are in fact true and the
argument is valid, then we call it sound.

Inductive arguments can be seen as strong
(the conclusion is more likely to be true because of support provided by the
premises) or as weak. When an
inductively strong argument does have true premises, we call it cogent.

How strong does an argument have to
be to be acceptable? A good rule to start with is that the more is at
risk, the more likely you want the conclusion to be correct. For
instance, in a civil case (the kind that occurs when one person sues another) a
jury is asked to decide between two sides based simply on the preponderance of
the evidence, and typically there can be a split decision among the
jurors. However, in a criminal case there is obviously more at stake (it
could be a person's freedom or possibly his life), and so the jury is asked to
decide unanimously on the basis of there not being a reasonable doubt about
their verdict. In everyday life, you would expect a stronger argument
about where to transfer for the last two years of college than you would about
what movie to see next weekend.

All arguments then can be classified as valid or
invalid. If valid, they are sound or unsound. If invalid, they are strong or weak and then, depending on the premises,
cogent or not cogent.Note that a strong argument by definition
cannot be valid, and a valid argument by definition cannot be strong.

Some additional notes: an
argument that misuses a form (what we will call a formal
fallacy) may not be valid but then we need to look at it in terms of
inductive strength. Also, an argument may be technically sound (valid
with acceptable premises) but still not a "good" argument because of
some informal fallacy (another kind of
mistake in the reasoning but one not related to the pattern). Most
typically this could be a problem of what we call begging the question, when
the premises would be acceptable only if someone already accepted the
conclusion as true. (We'll see more about this later on.)

In the first part of the course we are going to look more closely at the form
taken by deductive arguments that involve complete statements with a premise
expressed as a conditional relationship (one that can be restated with the
phrases "if" or "only if").

Inductive arguments can be seen as involving reasoning based on the
similarities of things or events (reasoning by analogy), reasoning based on
inferences from a limited group to a much larger one (inductive generalizations
and statistical arguments), reasoning about what is likely to take place in the
future or have taken place in the past (think of explanations such as those a
jury is called up to make in a trial), and especially reasoning that sets out
to decide cause and effect relationships. We will be looking at all this
in more detail in the second half of the course.

A final point to be considered is
how strong is a claim (the type of statement that might become a conclusion in
an argument). Saying that Jack will get a perfect score on his exam is a
stronger claim than saying he will do well on it. A good working rule for
evaluating arguments intended to prove such claims is that the stronger the
claim, the better the evidence should be. For instance, knowing that Jack
is a good student and is studying hard might be enough to justify saying he
will do well on his exam, but we would need more evidence before we can say he
will get a perfect score. We would have a much stronger case for this if
we also knew the test was comparatively easy.

Prepared by Professor Doug McFerran of Los Angeles Mission College. Professor Doug's text for
symbolic logic is available at Amazon.com. This page is part of a new text for courses in critical thinking.